Abstract: The main objects of Coding theory are metric vector or matrix spaces. Subsets of spaces are known as codes. The main problem is constructing codes of given pairwise distance and having maximal cardinality. Most known and most investigated spaces are Hamming spaces. Thousands papers and books are devoted to codes in the Hamming metric. We mention here only two books 1; 2 and will not consider this metric in details. Other metrics are investigated much less. In this paper, we give many examples of useful metrics. It is still non exhaustive review.

Keywords: metrics and norms, the uniform and non-uniform Hamming metrics, the Lee and Sharma-Kaushik? metrics, the city block (Manhattan) metric, the Varshamov metric, the burst metric, the 2-dimensional burst metric, the term rank metric, the rank metric, combinatorial metrics, projective metrics, graph metrics, the subspace metric.

ACM Classification Keywords: A.0 General Literature - Conference proceedings

MSC: 94B05, 94B20, 94B25

Link:

A BRIEF SURVEY OF METRICS IN CODING THEORY

Ernst Gabidulin

http://www.foibg.com/ibs_isc/ibs-25/ibs-25-p06.pdf